Electromagnetic dipole operator contribution to Bs → μ+μ−

The study of B-physics focuses on the properties and decays of B-mesons. It is essential for testing the Standard Model (SM) and investigating potential New Physics beyond the SM (BSM).
In this thesis, the focus is on the weak and rare decay, Bs → μ+μ−, considered a golden channel in the search for BSM physics. The current SM prediction for the branching fraction contains higher order Quantum-Chromodynamics (QCD) and weak corrections and is leading order in Quantum-Electrodynamics (QED).
The first part of this thesis focusses on diagrams that resolve the internal structure of the B-meson via exchange of a photon between the strange-quark and the final state muon. This is reflected in the dependence of the hadronic form factor on the Light-Cone-Distribution-Amplitude (LCDA) of the B-meson. In the Weak-Effective-Theory (WET), the flavor transition b → s is mediated by local operators. The electromagnetic dipole operator O_7 becomes particularly relevant in this thesis. The corresponding diagram is reanalysed from a theoretical perspective and calculated using the method of regions. The cancellation of endpoint divergences between different momentum regions is explicitly shown, and the rapidity logarithm is extracted. A factorization theorem is then provided, which must be renormalized by applying proper subtractions. The factorization theorems allows for the inclusion of QCD corrections. Firstly, building on the double-logarithmic term in the factorization theorem, leading-logarithmic (LL) QCD corrections are resummed to all orders in the strong coupling using renormalization-group evolution. Secondly, an explicit fixed-order calculation provides corrections to the relevant functions at next-to-leading order.
The second part of this thesis deals with strange-quark mass corrections of the LCDA, which serves as a hadronic input function in the context of QCD factorization of exclusive B-meson decays. In general it is not easy to be calculated and information are obtained in general from experimental data.
This thesis discusses the impact of a non-vanishing strange-quark mass on the LCDAs of B-mesons in the ``radiative tail''. Thereafter a numerical analysis of the LCDAs for different types of B-mesons is performed based on the inverse moment. A comparison with recent QCD sum-rule results is provided as a consistency check.